A VAE Approach to Sample Multivariate Extremes
This work addresses risk assessment for events like natural disasters and financial crashes, but it is incremental as it adapts existing VAE methods to a specific domain.
The paper tackled the problem of generating accurate multivariate extremes for risk estimation by proposing a VAE approach adapted for heavy-tailed distributions, showing improved learning of dependency structures compared to standard VAE and EVT-based methods on synthetic and real-world data.
Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the occurrence of natural disasters to financial crashes. Generative approaches from the machine learning community do not apply to extreme samples without careful adaptation. Besides, asymptotic results from extreme value theory (EVT) give a theoretical framework to model multivariate extreme events, especially through the notion of multivariate regular variation. Bridging these two fields, this paper details a variational autoencoder (VAE) approach for sampling multivariate heavy-tailed distributions, i.e., distributions likely to have extremes of particularly large intensities. We illustrate the relevance of our approach on a synthetic data set and on a real data set of discharge measurements along the Danube river network. The latter shows the potential of our approach for flood risks' assessment. In addition to outperforming the standard VAE for the tested data sets, we also provide a comparison with a competing EVT-based generative approach. On the tested cases, our approach improves the learning of the dependency structure between extremes.